The treadmill is fine to improve your conditioning and some of the benefits do translate to road running but as others have said on here it is not exactly the same.
If you have to use the treadmill I would use it for intervals but the intervals need to be a lot longer than 30 secs, try doing 800m intervals. To do 2.4km in 13 mins you need to run at 5:24 pace (5 mins 24 secs per km), or 11km per hour.
Try this, warm up for a couple of mins on the treadmill then run at 11km/hr for 800m, then jog for 200m, then run 12km/hr for 800m, then jog for 200m, then run 13km/hr for 800m then cool down for a few mins. Keep the treadmill in 1% incline.
Then when you can run outside just do a hard 3km run as the others on here have suggested.